The length of a rectangle is 6 inches more than its width, and its perimeter is 45 inches. Explain how to set up the equations and solve for the length and width of the rectangle.
Thank you so much please help asap!!

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calculista calculista · Answer 1 · 2020-02-12T09:17:12+01:00

Answer:

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

[tex]P=45\ in[/tex]

so

[tex]45=2(L+W)[/tex]

simplify

[tex]22.5=L+W[/tex] -----> equation A

The length of a rectangle is 6 inches more than its width

so

[tex]L=W+6[/tex] ----> equation B

Solve the system by substitution

substitute equation B in equation a

[tex]22.5=(W+6)+W[/tex]

solve for W

[tex]22.5=2W+6\\2W=22.5-6\\2W=16.5\\W=8.25\ in[/tex]

Find the value of L

[tex]L=W+6[/tex]

substitute the value of W

[tex]L=8.25+6=14.25\ in[/tex]

therefore

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches